Solve the system of equation. If the solution is dependent please write the answer in equation form. Show all the steps and Answer it in Ordered Triple? #x+2y-2z=3, x+3y-4z=6, 4x+5y-2z=3#.

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Answer 1 · 2017-08-09T15:20:04

The answer is #((x),(y),(z))=((-2z-3),(2z+3),(z))#

We perform the Gauss Jordan elimination with the augmented matrix

#((1,2,-2,:,3),(1,3,-4,:,6),(4,5,-2,:,3))#

#R3larrR3-4R1#, #=>#, #((1,2,-2,:,3),(1,3,-4,:,6),(0,-3, 6,:,-9))#

#R2larrR2-R1#, #=>#, #((1,2,-2,:,3),(0,1,-2,:,3),(0,-3, 6,:,-9))#

#R3larrR2+3R2#, #=>#, #((1,2,-2,:,3),(0,1,-2,:,3),(0,0, 0,:,0))#

#R1larrR1-2R2#, #=>#, #((1,0,2,:,-3),(0,1,-2,:,3),(0,0, 0,:,0))#

Therefore, the solutions are

#x=-2z-3#

#y=2z+3#

#z=#free